Extended calculations of energy levels and thermodynamic properties for hindered rotations of adsorbed molecules

Abstract

Energy levels and thermodynamic properties have been calculated for rotation of adsorbed molecules in two dimensions, hindered by a potential, V 2 sin 2 γ, where V 2 is the barrier height and γ is the angle between the principal molecular axis and the surface normal. For the three lowest energies, a perturbed rotational approximation agrees with an accurate, iterative solution when … V 2… is less than seven times the rotational constant, B. A perturbed, doubly-degenerate vibrational approximation agrees when V 2 is greater than 15 B. A perturbed one-dimensional vibration and one-dimensional rotation agree with the accurate solution when V 2 is less than — 7 B. At high temperatures, all thermodynamic properties approach those of a free rotor, provided the reference energy is the average potential energy over all angles. The heat capacity has a maximum (increasing with increasing … V 2… to 3R g 2 when V 2 is negative or to 2 R g when V 2 is positive) when the thermal energy, R g T, approximately equals 2…BV 2… 1 2 . When R g T is about 2…BV 2… 1 2 /3 and when … V 2… is much larger than B, the difference in heat capacity between hindered and free rotation becomes zero and the corresponding entropy difference reaches a minimum, whose depth increases logarithmically with … V 2/ B…. At low temperatures, the ortho-para separation factor has a linear Van't Hoff plot, whose slope and intercept reflect the energy and degeneracy, respectively, of the first excited state. Comparisons are made with experimental data on entropy of adsorption, ortho-para separation and rates of thermal desorption.